Question

A expressão i^13 + i^15 é igual a:
A)2i
B)i
C)-i
D)-2i
E)0

Answer 1

$i^{13}+i^{15}= \\ \\ divide~~expoente~~por~~4~~e~~eleva~~i~~ao~~resto \\ \\ i^{13}=13\div4=3~~resto~~1 \mapsto i^1 \\ \\ i^{15}=15\div4=3~~com~~resto~~3 \mapsto i^3=i^2.i=-1.i=-i \\ \\ lembra~~que~~i^2=-1 \\ \\ logo \\ \\ i^{13}+i^{15}=i+(-i)=i-i=0~~~~letra~~E$